As far back as 1967, only three-quarters of Americans said they would vote for an otherwise well qualified person who was a Mormon. This year – some 40 years later — the results to this question are almost exactly the same. ~USA Today/Gallup Blog
This reminds me of the remark you hear all the time in commentary on this question: in the 1968 election, George Romney didn’t face this problem. This is not true. He did face this problem, but failed to gain any ground as a presidential candidate before there was that much time for the issue to become a prominent one. We may forget, as we now enter the eleventh month of this election campaign (11 down, 11 to go!), that Romney started his campaign for the Republican nomination in November 1967 and by the end of February he was out. He was a declared candidate for a little over four months. He had made his famous “brainwashed” remark earlier in 1967 before becoming an avowedly antiwar candidate (an example his son has definitely not followed). His son started organising the preliminary elements of his presidential campaign in 2005, and there has been active speculation about his presidential run since mid-2006 at least. There has been much more time to ponder the implications of this factor, much more time to do a lot of polling on it, and much more time for pundits and bloggers to write endless commentaries on the topic.
The issue has taken on added significance in the nominating contest because evangelicals, many of whom would have been Democratic voters in 1967-68, have since started voting Republican much more frequently. As a Republican candidate before the 1968 realignment, Romney would have been more insulated from the early pressures his son is now experiencing. Had he been a Democrat, the issue might have become more significant in the nominating contest. Others cite the famed presidential runs of Mo Udall and Orrin Hatch, both of which went precisely nowhere in the end. Udall’s attempt was somewhat more successful, and even though Udall was also not an actively practicing Mormon his membership in the LDS church was used against him during the primaries. Udall lost to Jimmy Carter, so the Carter-Huckabee comparisons have something else going for them. Indeed, Udall’s defeat can provide some clue of what might have happened had Romney been running in the other party.
The idea that modern anti-Mormonism has somehow come out of nowhere in recent years is a myth.